I wonder if this person might be better served by some kind of bartering
software.

I wasn't sure there was such a thing -- but of course, there is.

http://www.curomuto.com/
http://www.barter-blog.com/?p=51

The problem is that they may lack an inventory function -- the book is here,
the book is there, oh wait ... this book is there but it should be here ...
ding that book ...

Not all that relevant when the object being exchanged is something like
"babysitting" or "lawn care".

Is it more like a community toolshare?  The only problem is that the "tools"
are not all in one place.

http://sourceforge.net/projects/toolshare/

This seems like a natural extension of something like Library Thing or the
Facebook book apps.  First, define a list of objects you hold that you want
to lend out.  Next define the group of people who can borrow said objects.
Finally, you need the inventory and tracking function.

Is it good enough for everyone in this group to just list their books on
Library Thing (or one of the Facebook apps) -- use that as you search
interface -- and then just have the borrower email the book owner directly
and ask for it?

Then you would also have to rely on the book owner to mark the item
unavailable and to mark it available again when it comes back.

Libraries can't do this because the number of borrowers is too high -- we
don't want to email with each person individually each time they want a
book.  And we need fast and precise control of our inventory and a quick way
(scanning) to check the item back in.

If each person is managing their personal book collection and lending it out
to a trusted circle -- you basically have a lot of librarians (each person
is a librarian) and not that many books.  You can ask your staff members to
do some work -- update the availability status of their books, ship their
books out, wait for the books to come back in, warn you if they haven't
arrived, tell you when they do.

You (the programmer) can focus on things like making requests easy to
initiate, automating reminder emails and making it really easy for each
librarian (meaning each owner of books) to do their few tasks above.  If
this group has policies, you'll want to enforce them -- for example, billing
someone if they admit that their pet monkey ate the book, nagging them a lot
or even kicking them out if they behave badly, not letting them borrow too
many things at once ... etc.

It would be cool if it could be programmed as an extension of one of the
apps above -- for example, it could draw from the Facebook book app list and
a group identity in a Facebook group ... now you've solved two of the three
problems above ...